How is risk of return measured in stock markets?

Question

How is risk of return measured in stock markets?

Answer 1

It is measured by the standard deviation of the daily annualised returns based on daily stock market prics. This is a statistical measure. The technical term is called BETA- beta for stock market index and beta for the individual stocks.

The beta coefficient, in terms of finance and investing, describes how the expected return of a stock or portfolio is correlated to the return of the financial market as a whole.

An asset with a beta of 0 means that its price is not at all correlated with the market; that asset is independent. A positive beta means that the asset generally follows the market. A negative beta shows that the asset inversely follows the market; the asset generally decreases in value if the market goes up.

Correlations are evident between companies within the same industry, or even within the same asset class (such as equities), as was demonstrated in the Wall Street crash of 1929. This correlated risk, measured by Beta, creates almost all of the risk in a diversified portfolio.

The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index.

To estimate Beta, one needs a list of returns for the asset and returns for the index; these returns can be daily, weekly or any period. Next, a plot should be made, with the index returns on the x-axis and the asset returns on the y-axis, in order to check that there are no serious violations of the linear regression model assumptions. The slope of the fitted line from the linear least-squares calculation is the estimated Beta. The y-intercept is the alpha.

There is an inconsistency between how beta is interpreted and how it is calculated. The usual explanation is that it gives the asset volatility relative to the market volatility. If that were the case it should simply be the ratio of these volatilities. In fact, the standard estimation uses the slope of the least squares regression line - this gives a slope which is less than the volatility ratio.